Convert files packed in Blend file
This is easily done with Python scripting, but I include in that statement a non-blender Python installation on your system. To do what you want from scratch:

Backup the blend file!

Go to python.org and download the latest Python (not the embeddable version).

Install Python on your system, and check the “add Python to PATH” when it comes up.

At the Command Prompt, type: python -m pip install pillow and it will download and install the Python imaging library (an easy way to convert the files).

In blender, unpack all images to one folder using the File menu (“use local directory” probably will work, but make sure nothing else is in there except the blend file).

Open IDLE (the Python IDE you just installed. You will see a Python shell.

Run the following code in that shell:
from PIL import Image NEWLINE
import glob NEWLINE
files=glob.glob(“C:\Users\Anthony\the_blend_directory_here\*”) NEWLINE
for f in files: NEWLINE
Image.open(f).save(f.replace(“.tga”, “.png”)) ENDOFLINE

The script should convert all unpacked images to png, one at a time. Close the Python shell upon verifying success.

In blender, go to the Scripting screen, and run the following code:
for img in bpy.data.images:
img.filepath=img.filepath.replace(“.tga”, “.png”)
img.reload()

Re-pack all files.

Delete the external images.